Higher genus quasimap wall-crossing for semi-positive targets

Abstract

In previous work (arXiv:1304.7056) we have conjectured wall-crossing formulas for genus zero quasimap invariants of GIT quotients and proved them via localization in many cases. We extend these formulas to higher genus when the target is semi-positive, and prove them for semi-positive toric varieties, in particular for toric local Calabi-Yau targets. The proof also applies to local Calabi-Yau's associated to some non-abelian quotients.

A missing correction term in genus 1 is now included in the statements of Conjectures 1.2.1-1.2.2. Minor changes in exposition, as suggested by the referee. Final version, to appear in JEMS

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• Quasimaps to GIT fiber bundles and applications
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